Capital budeting decisions with the Net Present Value rule
1. Foundations
Professor André Farber
Solvay Business School
University of Brussels, Belgium
Hanoi April 2000
1
Time value of money: introduction
• Consider simple investment project:
• Interest rate r = 10%
121
1
0
-100
Hanoi April 2000
2
Net future value
• NFV = +121 - 100  1.10 = 11
•
= + C1 - I (1+r)
• Decision rule: invest if NFV>0
• Justification: takes into cost of
capital
– cost of financing
– opportunity cost
+121
+100
0
-100
Hanoi April 2000
1
-110
3
Net Present Value
• NPV = - 100 + 121/1.10 = + 10
•
= - I + C1/(1+r)
•
= - I + C1  DF1
• DF1 = 1-year discount factor
•
a market price
• C1  DF1 =PV(C1)
+110
+121
• Decision rule: invest if NPV>0
-100
• NPV>0  NFV>0
-121
Hanoi April 2000
4
Internal Rate of Return
• Alternative rule: compare the internal rate of return for the
project to the opportunity cost of capital
• Definition of the Internal Rate of Return IRR : (1-period)
IRR = (C1 - I)/I
• In our example:
IRR = (121 - 100)/100 = 21%
• The Rate of Return Rule: Invest if IRR > r
Hanoi April 2000
5
IRR versus NPV
• In this simple setting, the NPV rule and the Rate of Return
Rule lead to the same decision:
• NPV = -I+C1/(1+r) >0
•  C1>I(1+r)
•  (C1-I)/I>r
•  IRR>r
Hanoi April 2000
6
IRR: a general definition
• -I + C1/(1+IRR)  0
• In our example:
• -100 + 121/(1+IRR)=0
•  IRR=21%
Net Present Value
• The Internal Rate of Return is
the discount rate such that the
NPV is equal to zero.
25.0
20.0
15.0
IRR
10.0
5.0
0.0
-5.0 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
-10.0
-15.0
-20.0
-25.0
Discount rate
Hanoi April 2000
7
Extension to several periods
• Investment project: -100 in year 0, + 150 in year 5.
• Net future value calculation:
NFV5 = +150 - 100  (1.10)5 = +150 - 161 = -11 <0
Compound interest
• Net present value calculation:
NPV = - 100 + 150/(1.10)5
= - 100 + 150  0.621 = - 6.86
0.621 is the 5-year discount factor DF5 = 1/(1+r)5
a market price
Hanoi April 2000
8
NPV: general formula
• Cash flows:
C0 C1 C2 … Ct … CT
• t-year discount factor: DFt = 1/(1+r)t
• NPV = C0 + C1 DF1 + … + Ct DFt + … + CT DFT
Hanoi April 2000
9
NPV calculation - example
• Suppose r = 10%
t
0
1
2
3
Cash flow
-100
30
60
40
Discount Factor
1 0.9091 0.8264 0.7513
PresentValue
-100.0 27.3 49.6 30.1
NPV
6.9
Hanoi April 2000
10
IRR in multiperiod case
• Reinvestment assumption: the IRR calculation assumes
that all future cash flows are reinvested at the IRR
• Disadvantages:
– Does not distinguish between investing and financing
– IRR may not exist or there may be multiple IRR
– Problems with mutually exclusive investments
• Advantages:
– Easy to understand and communicate
Hanoi April 2000
11
IRR and NPV - Example
Compute the IRR and NPV for the following two projects.
Assume the required return is 10%.
YearProject A
Project B
0
-$200
-$150
1
$200
$50
2
$800
$100
3
-$800
$150
NPV
42
91
IRR
0%, 100%
36%
Hanoi April 2000
12
Project A
Hanoi April 2000
1.
4
1.
2
1
0.
8
0.
6
0.
4
0
200.0
150.0
100.0
50.0
0.0
-50.0
-100.0
-150.0
0.
2
NPV Profiles
Project B
13
The Payback Period Rule
• How long does it take the project to “pay back” its initial
investment?
• Payback Period = # of years to recover initial costs
• Minimum Acceptance Criteria: set by management
• Ranking Criteria: set by management
Hanoi April 2000
14
The Payback Period Rule (continued)
• Disadvantages:
–
–
–
–
–
–
Ignores the time value of money
Ignores CF after payback period
Biased against long-term projects
Payback period may not exist or multiple payback periods
Requires an arbitrary acceptance criteria
A project accepted based on the payback criteria may not have a
positive NPV
• Advantages:
– Easy to understand
– Biased toward liquidity
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15
The Profitability Index (PI) Rule
•
•
•
•
PI = Total Present Value of future CF’s / Initial Investment
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria: Select alternative with highest PI
Disadvantages:
– Problems with mutually exclusive investments
• Advantages:
– May be useful when available investment funds are
limited
– Easy to understand and communicate
– Correct decision when evaluating independent projects
Hanoi April 2000
16
Incremental Cash Flows
• Cash, Cash, Cash, CASH
• Incremental
– Sunk Costs
– Opportunity Costs
– Side Effects
• Tax and Inflation
• Estimating Cash Flows
– Cash flows from operation
– Net capital spending
– Changes in net working capital
• Interest Expense
Hanoi April 2000
17
Summarized balance sheet
• Assets
• Fixed assets (FA)
• Working capital requirement (WCR)
• Cash (Cash)
• Liabilities
• Stockholders' equity (SE)
• Interest-bearing debt (D)
• FA + WCR + Cash = SE + D
Hanoi April 2000
18
Working capital requirement : definition
•
•
•
•
•
•
•
+
+
+
Accounts receivable
Inventories
Prepaid expenses
Account payable
Accrued payroll and other expenses
(WCR sometimes named "operating working capital")
– Copeland, Koller and Murrin Valuation: Measuring and
Managing the Value of Companies, 2d ed. John Wiley
1994
Hanoi April 2000
19
Interest-bearing debt: definition
• +
• +
• +
Long-term debt
Current maturities of long term debt
Notes payable to banks
Hanoi April 2000
20
The Cash Flow Statement
• Let us start from the balance sheet identity:
– FA + WCR + CASH = SE + D
• Over a period:
• FA + WCR + CASH = SE + D
• But:
SE =
STOCK ISSUE + RETAINED EARNINGS
= SI + NET INCOME - DIVIDENDS
FA =
INVESTMENT - DEPRECIATION
• (INV - DEP) + WCR + CASH = (SI + NI - DIV) + D
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21
•
•
•
•
•
•
•
•
•
•
(NI +DEP - WCR) - (INV) + (SI + D - DIV) = CASH

Net cash flows from
operating activities (CFop)

Cash flow from
investing activities (CFinv)

Cash flow from
financing activities (CFfin)
Hanoi April 2000
22
Free cash flow
• FCF = (NI +DEP - WCR) - (INV)
•
= CFop + CFinv
• From the statement of cash flows
• FCF = - (SI + D - DIV) + CASH
Hanoi April 2000
23
Understanding FCF
CF from operation + CF from investment + CF from financing = CASH
Cash flow from
operation
Cash flow
from financing
Cash flow from
investment
Cash
Hanoi April 2000
24
NPV calculation: example
•
•
•
•
•
•
•
•
•
Length of investment : 2 years
Investment
: 60 (t = 0)
Resale value
: 20 (t = 3, constant price)
Depreciation
: linear over 2 years
Revenue
: 100/year (constant price)
Cost of sales
: 50/year (constant price)
WCR/Sales
: 25%
Real discount rate
: 10%
Corporate tax rate
: 40%
Hanoi April 2000
25
Scenario 1: no inflation
Year
Sales
Cost of sales
EBITD
Depreciation
EBIT
Taxes
Net Income
0
1
100
50
50
30
20
8
12
2
100
50
50
30
20
8
12
12
30
25
12
30
0
17
42
Net Income
+ Depreciation
-DWCR
Investment
-60
Free cash flow -60
NPV
Hanoi April 2000
17.96 IRR
3
8
-8
-8
-25
20
37
24%
26
Inflation
• Use nominal cash flow
• Use nominal discount rate
• Nominal versus Real Rate (The Fisher Relation)
(1 + Nominal Rate) = (1 + Real Rate) x (1 + Inflation Rate)
•
•
•
•
•
•
•
Example:
Real cash flow year 1 = 110
Real discount rate = 10%
Inflation = 20%
Nominal cash flow = 110 x 1.20
Nominal discount rate = 1.10 x 1.20 - 1
NPV = (110 x 1.20)/(1.10 x 1.20) = 110/1.10 = 100
Hanoi April 2000
27
Scenario 2 : Inflation = 100%
Nominal discount rate:
(1+10%) x (1+100%) = 2.20
Nominal rate = 120%
NPV now negative. Why?
Year
Sales
Cost of sales
EBITD
Depreciation
EBIT
Taxes
Net Income
0
1
200
100
100
30
70
28
42
2
400
200
200
30
170
68
102
42
30
50
102
30
50
22
82
Net Income
+ Depreciation
-DWCR
Investment
-60
Free cash flow -60
NPV
Hanoi April 2000
-14.65 IRR
94%
3
64
-64
-8
-100
160
196
28
Decomposition of NPV
–
–
–
–
–
–
EBITD after taxes
Depreciation tax shield
WCR
Investment
Resale value after taxes
NPV
52.07
20.83
-3.94
-60
9.02
17.96
Hanoi April 2000
52.07
7.93
-23.67
-60
9.02
14.65
29